A device of this type is known, particularly by French Pat. No. 2 109 189. The tool holder disclosed therein presents a bearing face and two stop faces in dihedral form perpendicular to said bearing face, in order to receive the insert. This known device comprises a screw of which the threaded shank adapted to be screwed in a tapped hole in the tool holder, passes through a cylindrical hole in the insert which is eccentric when the latter is suitably positioned in contact with the faces mentioned above and without the wall of this eccentric hole touching the shank of the screw. The head of this screw presents a truncated bearing surface cooperating with an annular portion of a likewise truncated bearing surface bordering the eccentric hole of the insert in order to press the sides thereof against the stop faces of the tool holder and concomitantly to clamp said insert against the bearing face of said tool-holder.